Abstract

Settling an open problem that is over ten years old, we show that
Manhattan channel routing---with doglegs allowed---is NP-complete when
all nets have two terminals. This result fills the gap left by
Szymanski, who showed the NP-completeness for nets with four
terminals. Answering a question posed by Schmalenbach and Greenberg,
Jájá, and Krishnamurty, we prove that the problem remains
NP-complete if in addition the nets are single-sided and the density
of the bottom nets is at most one. Moreover, we show that Manhattan
channel routing is NP-complete if the bottom boundary is irregular and
there are only 2-terminal top nets. All of our results also hold for
the restricted Manhattan model where doglegs are not allowed.